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arXiv · 2006.02345

On the structure of some locally nilpotent groups without contranormal subgroups

Leonid A. Kurdachenko·Patrizia Longobardi·Mercede MAJ
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Abstract

Following J.S. Rose, a subgroup H of a group G is said contranormal in G if G = H^G . In a certain sense, contranormal subgroups are antipodes to subnormal subgroups. It is well known that a finite group is nilpotent if and only if it has no proper contranormal subgroups. We prove that a nilpotent-by-finite group with no proper contranormal subgroup is nilpotent. There are locally nilpotent groups with a proper contranormal subgroup. We study the structure of hypercentral groups with a finite proper contranormal subgroup.

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Leonid A. Kurdachenko, Patrizia Longobardi, Mercede MAJ. 2020-06-03. On the structure of some locally nilpotent groups without contranormal subgroups. https://arxiv.org/abs/2006.02345

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